...+ 7axt+xt Examining the formation of the above coefficients, we observe, that each coefficient was found by multiplying the coefficient of the preceding' term by the exponent of the leading quantity a in that term, and dividing the product by the number which marks the place of that...

...and —x* raised to the nth power is either + *""* or — *mn, according as n is even or odd. is got by multiplying the coefficient of the preceding term by the exponent of the leading quantity in that term, and dividing the product by the number of that term. 5. That when the...

...co-efficient of any term from the co-efficient of the preceding term. The co-efficient of any term is formed by multiplying the co-efficient of the preceding term by the exponent of x in that term, and dividing the product by the number of terms which precede the required term. For...

...(x-|-a) 8 is 2, of (.rf a) 6 is 6, of (x+a) 7 is 7. IV. The coefficient of any term after the second may be found by multiplying the coefficient of the preceding term by the index of x in that term, and dividing by the number of terms preceding the required term. Thus, in...

...is 4, the same number as the given power. The coefficient of the third term is 6, and it is obtained by multiplying the coefficient of the preceding term by the exponent of the a, and dividing this product by 4x3 2, the number of this term ; thus — ~ — =6. The coefficient...

...second term (ie of both x and a) is n. (5.) The coefficient of any term whatever after the first is found by multiplying the coefficient of the preceding term by the exponent of the leading quantity in that term, and dividing by the number of terms preceding the required term. a.)...

...OF COEFFICIENTS. The coefficient of the first term is 1 / the coefficient of any succeeding term is found by multiplying the coefficient of the preceding term by the exponent of tJie leading letter in that term, and dividing the product by the number of terms preceding the required...

...second term is the same as the exponent of the power ; and, in general, the coefficient of any term is found by multiplying the coefficient of the preceding term by the exponent of the leading letter of the same term, and dividing the product by the number which marks its place. NOTE...

...coefficient of the leading quantity in the root. UNIVERSALLY; — The coefficient of any term may be obtained by multiplying the coefficient of the preceding term by the exponent of the leading quantity in that term, or by (he number of the term from the last, and, by the coefficient...

...coefficient of the leading quantity in the root. UNIVERSALLY; — The coefficient of any term may be obtained by multiplying the coefficient of the preceding term by the exponent of the leading quantity in that term, or by the number of the term from the last, and by the coefficient of...